Ariel Rubinstein (NYU & Tel Aviv Uni) has a neat piece in the latest issue of the Economic Journal, in which students are asked to solve a firm optimisation problem, deciding how many workers a firm should fire. The profit maximising decision involves a lot of layoffs, but the firm can still make a profit with zero layoffs. He shows that if shown a table, students are likely to fire fewer workers. But if they are shown the mathematical formula relating layoffs to profits, they are likely to fire more workers. He concludes:

In any case, we need to re-evaluate the use of mathematical exercises which lead students to focus on the task of maximisation rather than on real economic problems. In the best case, these mathematical exercises simply make the study of economics less interesting; in the worst case, they contribute to the shaping of a rather unpleasant ‘economic man’.

Doesn’t it depend on the wording of the question?
if it asks how to acheive the maximum profit, then the math’s answer would be correct.

if it asked how to make <a> profit, then both might be correct.

It also supposed that laying people off is a ‘ bad’ thing, where in fact it might be the best for everyone concerned. especially if it results in the people bouncing into new jobs quickly (which does happen in high-demand industries, or people who have mobile skill sets)